Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33816 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#2215 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
502 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24)(22,26)(28,29)(30,39)(31,36)(32,35)(33,46)(34,40)(37,45)(38,44)(41,47)(42,49)(43,51)(48,57)(50,55)(52,59)(53,58)(54,56);(20,21)(22,25)(23,24)(26,27)(28,30)(29,34)(31,40)(32,41)(33,42)(35,50)(36,39)(37,48)(38,49)(43,55)(44,56)(45,58)(46,54)(47,51)(52,53)(57,59);(21,24)(25,27)(29,35)(30,40)(32,45)(33,44)(34,47)(36,51)(37,38)(39,50)(41,57)(43,59)(46,52)(48,54)(49,53)(55,58);(20,22,23,26)(21,25,24,27)(29,36)(34,39)(35,51)(37,52)(38,46)(47,50)(48,53)(49,54)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26804);